SU (9) Family Unification S. Nandi Oklahoma State University and - PowerPoint PPT Presentation

SU (9) Family Unification S. Nandi Oklahoma State University and Oklahoma Center for High Energy Physics (in collaboration with J. Dent and T. W. Kephart) arXiv: 0908.3915[hep-ph] (to appear in Phys. Lett. B) Talk at PHENO 2010, Madison, Wisconsin, May, 2010 S. Nandi SU (9) Family Unification

Goals To present a SU (9) model of family unification with 3 light chiral families. To provide a natural hierarchy for the charged fermion masses and mixings. To link the scale of the tiny neutrino masses with the hierarchy of the quark masses and mixings. S. Nandi SU (9) Family Unification

Outline of Talk Introduction Model and the Formalism Phenomenological Implications Conclusions and Outlook S. Nandi SU (9) Family Unification

Introduction 3 light families of quarks and leptons 5 orders of magnitude hierarchy among the charged fermion masses 2 orders of magnitude hierarchy among the quark mixing angles Neutrino masses are 7 orders of magnitude smaller that the lightest charged fermion masses S. Nandi SU (9) Family Unification

Introduction Our approach Use SU (5) as one family GUT Enlarge the symmetry to SU ( N ) , N > 5 , to include more families Use only anti-symmetric representations of SU (9) ⇒ only 5 , ¯ 5 , 10 , ¯ 10 , 1 Choose a set of anti-symmetric representations such that ⇒ 3( ¯ 5 + 10 ) + n 1 ( 5 + ¯ 5 ) + n 2 ( 10 + ¯ 10 ) + n 3 ( 1 ) ( 5 + ¯ 5 ) , ( 10 + ¯ 10 ) , and 1 in the GUT scale ⇒ only 3(¯ 5 + 10 ) light families of fermions S. Nandi SU (9) Family Unification

Introduction Questions: How to generate fermion masses and mixing hierarchy? How to suppress FCNC processes? How to explain m ν ≪ m q , m l ? or how to generate m N R /M GUT = 10 − 2 ? S. Nandi SU (9) Family Unification

Introduction Our philosophy Use additional discrete symmetries to arrange the hierarchy of the Yukawa couplingss Only top quark have dim 4 Yukawa coupling Yukawa couplings of the lighter quarks will appear successively as higher dimensional operators Link the neutrino mass scale to the suppression of these Yukawa couplings S. Nandi SU (9) Family Unification

Model & Formalism Our concrete model Gauge Symmetry: SU (9) Use additional discrete symmetries, Z 2 , Z ′ 2 , Z ′′ 2 , and Z 3 to constrain the Yukawa couplings suitably Only top quark has dim 4 Yukawa coupling Yukawa couplings of all other quarks are successively higher dimensional (hence suppressed), and are constrained by the above symmetries Supression factor, ε = V S /V GUT where V S = VeV of an SU (5) singlet Higgs field, and V GUT = GUT scale VeV. S. Nandi SU (9) Family Unification

Model & Formalism F = 126 + 84 + 2( 36 ) + 14( ¯ 9 ) Note that this assignment is anomaly free. 126 → 5 + 4( 10 ) + 6( 10 ) + 4( ¯ 5 ) + 1 84 → 10 + 4( 10 ) + 6( 5 ) + 4( 1 ) 36 → 10 + 4( 5 ) + 6( 1 ) 9 → ¯ ¯ 5 + 4( 1 ) Hence the complete set of fermions in the model is F = 3( 10 + ¯ 5 ) F + 15( 5 + ¯ 5 ) F + 7( 10 + 10 ) F + 73( 1 ) F . ⇒ 3 light families of fermions. S. Nandi SU (9) Family Unification

Model & Formalism Assignment of three chiral families: ¯ 3rd family : ( 126 3 ) F → t L , t R , b L 9 3 → b R ¯ 2nd family : 84 2 → c L , c R , s L 9 2 → s R ¯ 1st family : 36 1 → u L , u R , d L 9 1 → d R In addition, the Higgs represetations that we shall use are 36 H , 36 ′ H , 36 ′′ H , 9 H , and 315 H . S. Nandi SU (9) Family Unification

Model & Formalism Charges under the discrete symmetries: Z 2 Z ′ Z ′′ Z 3 2 2 (126 3 ) F − 1 (84 2 ) F − 1 (36 1 ) F − 1 (9 3 ) F α (9 2 ) F − 1 (9 1 ) F − 1 − 1 α 36 H 36 ′ − 1 H 36 ′′ α H 9 H − 1 − 1 315 H S. Nandi SU (9) Family Unification

Model& and the Formalism Allowed Yukawa interactions: � (126 F ) 2 315 H D = 4 : tt :  cc : (84 2 ) F (84 2 ) F 36 H 315 H   (126 3 ) F (84 2 ) F [36 H 315 H + (315) 2 D = 5 : ct = tc : H ]  (126 3 ) F (¯ bb : 9 3 ) F 36 ′ H 36 ′′  H  (126 3 ) F (36 1 ) F [(36 H ) 2 + (36 ′ H ) 2 ] (36 H ) tu = ut :    (84 2 ) F (36 1 ) F 36 H [(9 H ) 2 + (315 H ) 2 ]  cu = uc :     (126 3 ) F (¯  9 2 ) F 36 H 36 ′ bs : H 9 H  D = 6 : H ) 2 36 ′ (¯ 9 3 ) F (84 2 ) F (36 ′′ sb :  H   (84 2 ) F (¯ 9 2 ) F 36 ′  ss : H 9 H 315 H    H ) 2 9 H  (126 3 ) F (¯  bd : 9 1 ) F (36 ′′  S. Nandi SU (9) Family Unification

Model& and the Formalism Allowed Yukawa interactions (continued):  (36 1 ) F (36 1 ) F (9 H ) 2 315 H 36 H uu :    H ) 2 9 H (36 1 ) F (¯ H (36 ′′  dd : 9 1 ) F 36 ′  D = 7 : H ) 2 315 H (36 1 ) F (¯ H (36 ′′ db : 9 3 ) F 36 ′    (84 2 ) F (¯  9 1 ) F 36 H 36 ′ H 36 ′′ sd : H 9 H  S. Nandi SU (9) Family Unification

Phenomenological Implications Up and down quark mass matrices h u 11 ε 3 h u 12 ε 2 h u 13 ε 2   h u h u h u  v. 21 ε 2 M u = 22 ε 23 ε  h u 31 ε 2 h u h u 32 ε 33 h d h d h d  11 ε 3 12 ε 3 13 ε 3   v . h d 21 ε 3 h d 22 ε 2 h d 23 ε 2 M d =  h d 31 ε 2 h d 32 ε 2 h d 33 ε S. Nandi SU (9) Family Unification

Phenomenological Implications Quark and lepton masses, CKM mixing, FCNC and Higgs Decays Existence of 3 light families from a gauge SU (9) family symmetry Parameters of the model: h u ij , h d ij , ε = V S /V GUT With choices h u ij , h d ij ∼ O (1) , and ε ∼ 1 / 50 , good agreement with all the quark and charged lepton masses. No SM singlet Higgs at the EW scale (Our singlet Higgs are close to the GUT scale) Yukawa coupling matrices and the mass matrices are proportional ⇒ No FCNC as in SM SM Higgs boson decays are identical to those in SM S. Nandi SU (9) Family Unification

Phenomenological Implications Neutrino masses and mixings ¯ 9 of SU (9) ⇒ ¯ 5 F + 4( 1 ) F Singlet fermions are unavoidable Existence of RH neutrinos are required in our model this is similar to SO (10) GUT, but we have a family unification gauge symmetry Mass scale for these RH neutrinos are linked to the suppression factor needed to explain charged fermion mass hierarchy and CKM mixings, ε = V S /V GUT ⇒ M R ∼ 10 14 GeV, as required to explain the observed light neutrino masses via see-saw S. Nandi SU (9) Family Unification

Conclusions Presented a family unification model with three light chiral families Based on SU (9) gauge symmetry with additional discrete symmetries Generate the hierarchy of quark and charged lepton masses, and CKM mixings SM singlet neutrinos are unavoidable Links the scale of the RH singlet neutrinos ∼ 10 14 GeV to quark mass hierarchy and mixings S. Nandi SU (9) Family Unification